multi-robot systems “the mob has many heads but no brains”. -- english proverb

Multi-Robot SystemsMulti-Robot Systems

“The mob has many heads but no brains”. -- English Proverb.

Today's’ Objectives

To understand some of the problems being studied with multiple robots

To understand the challenges involved with coordinating robots

To investigate a simple behaviour-based self-organization strategy for a common application

To investigate a simple communication strategy

Why Multiple Robots?Faster execution

More robust

Simplify design of robots

Task requires it

larger range of task domains

greater efficiency

improved system performance

fault tolerance

lower economic cost

ease of development ???

distributed sensing and action

Why Not Multiple Robots?

More communicationMore complexityHarder to testN x the troubleExpensivePerformance depends on issues

involving interaction between robots

Interactions complicate development

Difficult to model group behaviors from top down (i.e., centralized control) when environment is unknown and/or dynamic

Sensor and/or physical interference

Research 5 major themes of robot group research:

Group control architecture- decentralization and differentiation

Resource conflict resolution- e.g., space sharing

Origin of cooperation- i.e, genetically−determined social behavior or

interaction−based cooperative behavior Learning

- e.g., control parameter tuning for desired cooperation Geometric problem solving

- e.g., geometric pattern formation

A typical research paper will focus on only one theme (or aspect) of group robotics.

A typical research paper will focus on only one theme (or aspect) of group robotics.

Research What kinds of problems have been studied:

Multi-robot path planning Traffic control Formation generation, keeping and control Target tracking Multi-robot docking Box-pushing Foraging Multi-robot soccer Exploration and localization Transport

Example research in multi-robot systems

(CMU) Mapping(CMU)Soccer

(UPenn) Formations

More example research in multi-robot systems …

(Dartmouth/MIT)Reconfiguration

(USC) Mapping

(U. Tennessee)Mobile Sensor NetDeployment

iRobotSwarms

Terminology Terminology

Various rather interchangeable terms are used: Group behavior / robotics Collective behavior / robotics Cooperative behavior / robotics Swarm robotics Multi-robot systems

Popular and recent area of study due to

wide-range of possible application areas

Cooperative vs. CompetitiveCooperative vs. Competitive

Cooperative: picking up a heavy load

Competitive: RoboSoccer

Recently, more focus on cooperative form not competitive.

Why Multiple Robots?

Some tasks require a team Robotic soccer

Some tasks can be decomposed and divided for efficiency Mapping a large area

Many specialists preferable to one generalist Increase robustness with redundancy Teams of robots allow for more varied and

creative solutions

Multi-robot Application Areas

Automated warehouse management Automatic Guided Vehicle (AGV) Systems Planetary exploration Automatic construction Robotic cleanup of hazardous sites Agriculture Military Applications RoboCup

Multi-Robot Systems : Brains vs. Bodies

Typical Tasks for Multi-Robot Teams - I

Mapping and exploration Hazardous clean-up Reconnaissance Tracking

Map created by robot team.

Loosely-coordinated

Typical Tasks for Multi-Robot Teams - II

Carrying objects Robot soccer Large-scale construction Constrained exploration Coordinated Reconn.

RoboticConstruction.

Tightly Coordinated

Box Carrying

Analogy with Traveling Salesman Problem (TSP)

Lots of cities, lots of salesmen Distribute cities to salesmen so total

distance is minimized. What domains have TSP?

Pittsburgh

Chicago

New York

LA

Houston

Robot Task Allocation

How do we assign the cities (tasks) to the salesmen (robots)? Ideas?

Motion Coordination

Lots of types of motion coordination:

Relative to other robots: E.g., formations, flocking, aggregation, dispersion…

Relative to the environment: E.g., search, foraging, coverage, exploration …

Relative to external agents: E.g., pursuit, predator-prey, target tracking …

Relative to other robots and the environment: E.g., containment, perimeter search …

Relative to other robots, external agents, and the environment:

E.g., evasion, soccer …

Most Commonly Studied Tasks for Multi-Robot Systems

Foraging Consider a common problem studied in robotic colonies, foraging:

gathering/collecting items

- possibly bringing them to some specific location(s) (e.g., to particular room) or general locations(s) (e.g., to outer walls).

there are many variations of this problem

Consider a specific instance: robots can detect when it finds an item and can push it to some

location (or pick it up and drop it off). robots will be encoded with a fixed, instinctive behavior and thus

will not learn “how” to forage.

Foraging Consider allowing robots to move randomly in an

environment with no cooperation.

Robots must find forage items (e.g., when passing over them) and bring them to the boundaries.

Robots may collide, which

may interrupt the forage

procedure of a robot.

Eventually, over time,

each forage item will be

found by some robot:

Foraging

As more robots are used,

the speed of forage

completion increases.

The performance decreases

when the forage items are

not evenly distributed.

this is because robots are

not directed towards forage

items, only finding them by

chance.

Foraging Performance Over Time - Random Movement with Evenly Spread Forage Items

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Increasing Time ====>

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Foraging Performance Over Time - Random Movement with Clustered Forage Items

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Foraging

Intuitively, performance can be improved by: reducing collisions (or interference) between robots preventing robots from traveling over the same areas directing robots towards clusters of forage items

The obvious way of reducing collisions and preventing duplicate travel is to distribute robots by explicitly assigning each one a particular area in the environment in which to forage.

environment broken down into “equal−sized”

areas which are assigned to individual robots

Foraging – Explicit Distribution This strategy has advantages:

+ ensure even distribution of robots

- good when items to be foraged are evenly distributed randomly

+ minimizes sensor interference and physical collisions between robots

and disadvantages:

- requires robots to “know” and maintain specific positions

- requires knowledge of environment

- expensive sensors ?? (e.g., GPS)

- expensive computation (e.g., position estimation)

- can be inefficient if forage items are clustered

A simple way of determining the foraging areas for each robot is to base the regions on the dual graph:

Recursively divide dual graph in “half” until number of regions

matches the number of robots:

Foraging – Explicit Distribution

Each robot remains in its own designated area.

Each robot remains in its own designated area.

Foraging – Explicit Distribution Performance (i.e., speed of forage completion) is highly dependant

on shape of environment and location of forage items.

With clustered forage items, most robots become useless if forced to remain in a particular area.

With clustered forage items, most robots become useless if forced to remain in a particular area.

With forage items evenly distributed, robots work effectively in near optimal configuration, provided that robots do not have to leave their environment to complete the task.

With forage items evenly distributed, robots work effectively in near optimal configuration, provided that robots do not have to leave their environment to complete the task.

Foraging – Implicit Distribution Clearly, fixing the locations of each robot

may not be the best choice if:

the distribution of forage items is not known

to be random and evenly distributed

the robots must travel outside their areas to complete

the forage task (i.e., to deliver their payload).

A compromise is to hard−code specific behavioral rules into the robots that minimize their collisions and attempt to keep them distributed.

Foraging – Implicit Distribution Consider robots with omni−directional beacons which are detectable

from other nearby robots: robots avoid moving towards nearby beacons intuitively, robots should remain separated/distributed

When other robot detected within sensor range, robot moves in opposite direction.

When other robot detected within sensor range, robot moves in opposite direction.

With multiple beacons, either move away in combined vector direction or away from strongest signal.

With multiple beacons, either move away in combined vector direction or away from strongest signal.

Although robots may still re−encounter other robots during their movements, in general they remain distributed.

Although robots may still re−encounter other robots during their movements, in general they remain distributed.

Foraging – Comparison A comparison of these schemes shows that:

for evenly spread forage items there is no significant advantage of either scheme in terms of forage completion time and the simple random movement seems to do well.

for clustered forage items the fixed area scheme performs poorly with few robots and the repel scheme performs better

Scheme Comparison - 25/12/4 RobotsEvenly Spread Forage Items

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Fixed (25 robots)

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Scheme Comparison - 25/12/4 RobotsClustered Forage Items

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Repel scheme favorable since performs well AND minimizes robot contact.

Repel scheme favorable since performs well AND minimizes robot contact.

Foraging – Improvement A more significant improvement can be made if something is known

about the forage items (e.g., they are clustered).

can “signal” other robots

when item is encountered

leave signal on until:

- fixed amount of time elapses

- other robots come nearby

can either wait stationary

or continue moving

Robot turns on beacon when item is found.

Robot turns on beacon when item is found.

Robots within beacon’s range will travel toward nearest beacon.

Robots within beacon’s range will travel toward nearest beacon.

Robots outside of beacon’s range will continue moving randomly.

Robots outside of beacon’s range will continue moving randomly.

Following / Swarming / Flocking / Schooling

Natural flocks consist of two balanced, opposing behaviors: Desire to stay close to flock Desire to avoid collisions

with flock

Why desire to stay close to flock? In natural systems:

Protection from predators Statistically improving

survival of gene pool from predator attacks

Profit from a larger effective search pattern for food

Advantages for social and mating activities

How do formations work?

Alignment: steer towardsaverage heading of local flockmates

Cohesion: steer to move towardthe average position of localflockmates

Separation: steer to avoidcrowding local flockmates

Multi-Robot Communication Taxonomy

Communication range: None Near Infinite

Communication topology: Broadcast Addressed Tree Graph

Communication bandwidth High (i.e., communication is essentially “free”) Motion-related (i.e., motion and communication costs are about the same) Low (i.e., communication costs are very high Zero (i.e., no communication is available)

Explicit Communication

Defined as those actions that have the express goal of transferring information from one robot to another

Usually involves: Intermittent requests Status information Updates of sensory or model information

Need to determine: What to communicate When to communicate How to communicate To whom to communicate

Communications medium has significant impact Range Bandwidth Rate of failure

“Help, I’m stuck”

Implicit Communication

Defined as communication “through the world” Two primary types:

Robot senses aspect of world that is a side-effect of another’s actions

Robot senses another’s actions

1. Truck leaves with full load

2. Awaiting truck knows it isOK to move into position

Three Key Considerations in Multi-Robot Communication

Is communication needed at all?

Over what range should communication be permitted?

What should the information content be?

Is Communication Needed At All?

Keep in mind: Communication is not free, and can be unreliable In hostile environments, electronic countermeasures may be in

effect

Major roles of communication: Synchronization of action: ensuring coordination in task ordering Information exchange: sharing different information gained from

different perspectives Negotiations: who does what?

Many studies have shown: Significantly higher group performance using communication However, communication does not always need to be explicit

Over What Range Should Communication Be Permitted?

Tacit assumption: wider range is better

But, not necessarily the case

Studies have shown: higher communication range can lead to decreased societal performance

One approach for balancing communication range and cost Probabilistic approach that minimizes communication delay time

between robots Balance out communication flow (input, processing capacity, and

output) to obtain optimal range

What Should the Information Content Be?

Research studies have shown: Explicit communication improves performance significantly in

tasks involving little implicit communication

Communication is not essential in tasks that include implicit communication

More complex communication strategies (e.g., goals) often offer little benefit over basic (state) information “display” behavior is a rich communication method

In summary….A Good Multi-robot System Is: Robust: no single point of failure Optimized, even under dynamic conditions Quick to respond to changes Able to deal with imperfect communication Able to allocate limited resources Heterogeneous and able to make use of

different robot skills

The Coordination Spectrum

Loosely-Coordinated Tightly Coordinated Decomposable into

subtasks Independent execution Minimum interaction Task decomposition and

allocation strategies.

Tasks not decomposable Coordinated execution Significant Interaction

Basic Approaches

Centralized Attempting optimal plans

Distributed Every man for himself

Market-based

Taxonomy of Approaches

CentralizedAttempting optimal plans

DistributedEvery man for himself

Emergent HybridIntentional

Reactive Behavior-Based

Fully Centralized

Centralized Allocation

Market Based

Fully Centralized

Single agent “leader“ plans for entire team

Robot team treated as a single “system” with many degrees of freedom

Leader plans optimal actions for group Group members send information to

leader and carry out actions

Potential to be optimal Implicitly encodes coordination– Usually computationally intractible– Single point of failure– Slow to respond to changes

Leader can take all relevant information into account

In theory, coordination can be perfect: Optimal plans possible!

Centralized Methods: Pros

Computationally hard Intractable for more than a few robots

Makes unrealistic assumptions: All relevant info can be transmitted to leader This info doesn’t change during plan construction

Result: response sluggish or inaccurate Vulnerable to malfunction of leader Heavy communication load

Centralized Methods: Cons

Centralized Allocation

Single agent assigns tasks to teammates Teammates complete tasks individually Execution is distributed Allocation can be optimal– Still computationally expensive– Still has single point of failure

Distributed Approaches

Planning responsibility spread over team Each robot basically independent Robots use locally observable information to

make their plans

Distributed Methods: Pros

Fast response to dynamic conditions Little or no communication required Little computation required Smooth response to environmental changes Very robust

No single point of failure

Distributed Methods: Cons

Not all problems can be decomposed well Plans based only on local information Result: solutions are often highly sub-optimal

Emergent Multi-robot systems require efficient and accurate planning Global optimal solutions are expensive

communication overhead planning time

Solution: An emergent approach Emergent: Solution results from interactions of robots Local approximation to global optimal Low cost and feasible in real-time

Task

Distribution

Task

Distribution

Reactive

Robots have a tight sense-act loop

Extremely fast Very simple– Cannot handle

complex tasks

Behavior-based

Use state information to choose actions

Fast, simple Robots can contribute

to multiple tasks More expressive than

reactive— Still cannot plan

Intentional

Communication with the intent to coordinate

Facilitates planning, scheduling

Better solutions– Slow in time-critical

situations– Very dependent on

communication

Box

Pushers

Watcher

Goal

Hybrid Emergent approach in larger

intentional approach Allows better

planning/distribution of resources

Can have tight coordination– Cannot have complex

interactions

Robot Formation: Distributed vs. Central Control

Performance Measure : Cumulative Formation Error

Four Different Strategies:

Strategy I: Local Control OnlyStrategy II: Local Control Augmented by Global GoalStrategy III: Local Control Augmented with Global

Goal and Partial Global Information

Strategy IV: Local control augmented by global goal and more complete global information

Simulation of mission involving formation maintenance while moving to goal

4 different strategies with increasing global control

Quantitatively measured via deviation from the formation and time taken to reach goal

Strategy I: Local Control Only

–Effective for smooth trajectories

–Sharp turns cause formation to break up due to local control

Robots maintain their position by staying a fixed distance from a certain side of neighbor

Strategy II: Local Control Augmented by Global Goal

–Robots given knowledge of global goal: Maintain line formation

–Robot D now moves to a more globally appropriate position

–May be inappropriate if B is merely avoiding obstacle

Strategy III: Local Control Augmented with Global Goal and Partial Global Information

–At time of robot B’s turn, other robots are informed of destination of waypoint X

Strategy IV: Local control augmented by global goal and more complete global information

–Robots are given complete knowledge of leaders route

–Allows other robots to predict future positions of the leader and resulting positions for themselves

Simulation Results

Market-based Approach:The Basic Idea

Based on the economic model of a free market

Each robot seeks to maximize individual “profit”

Robots can negotiate and bid for tasks Individual profit helps the common good Decisions are made locally but effects

approach optimality Preserves advantages of distributed approach

In other words, Robots model an economy:

Accomplish task receive revenue Consume resources incur cost Robot goal: maximize own profit Trade tasks and resources over the market

(auctions, etc.) By maximizing individual profits, team finds

better solution Time permitting, more centralized Limited computational resources, more

distributed

$

$

$

$$

Analogy To Real Economy

Robots must be self-interested Sometimes robots cooperate, sometimes they

compete Individuals gain benefits of their good

decisions, suffer consequences of bad ones Just like a real market economy, the result is

global efficiency

How Do We Determine Profit?

Profit = Revenue – Cost Team revenue is sum of individual revenues,

and team cost is sum of individual costs Costs and revenues set up per application

Maximizing individual profits must move team towards globally optimal solution

Robots that produce well at low cost receive a larger share of the overall profit

Goal: Task Allocation

Efficient Scalable Fault-tolerant Works for heterogeneous physical robots

Resource Allocation

Not a planning problem Not a task-execution problem Equivalent to conjunctive planning (NP-C)

A set of propositions which share variables and must be satisfied simultaneously

Auction methods are applicable Not yet demonstrated on real-life task settings

Auction Protocol Announcement (when new task comes in) An agent acts as ``auctioneer'' by publishing an announcement

message for the task. The message contains details about the task, such as its name, length, and a new subject on which to negotiate it. The message is addressed to the set of subjects which represent the resources required to execute the task; thus only those robots currently capable of performing the task will receive the message

Auction Protocol Metric evaluation: Since there may be more than one capable

robot available for a given task, we need a method for deciding among them. This decision process is the very basis of achieving effective task allocation; the goal is to allocate each task to the most fit robot. Thus the announcement also includes metric(s) with which each candidate robot can determine its fitness . Announcement includes fitness metric Robots evaluate themselves

Auction Protocol Bid submission - After evaluating the appropriate

metric(s), each candidate robot publishes its resulting task-specific fitness "score" as a bid message

Each robot publishes score

Auction Protocol Close of auction - After sufficient time has passed,

the auctioneer processes the bids, determines the winner, and notifies the bidders with a close message. The winner is awarded a time-limited contract to execute the task and the losers return to listening for new tasks.

Auction Protocol Progress monitoring/contract renewal - While the winner executes

the task, the auctioneer monitors task progress. Assuming sufficient progress is being made, the auctioneer periodically sends a renewal message to the winner, which responds with an acknowledgment message, until the task is completed.

Experiment: Loose Cooperation

Random tasks object-tracking (camera, mobile) sentry-duty (camera, laser, mobile) cleanup (camera, bumpers, mobile) monitor-object (overhead-camera)

Results Optimal allocation Low bandwidth usage (mean: 0.66 kb/s) Task allocated whenever resources available

Experiment: Box Pushing

Tightly-coupled cooperation Pushers cannot see goal Watcher cannot push box Watcher communicates directions to pushers Results:

Efficient paths Consistent execution Fault-tolerance

Fault-Tolerance

Communication is by anonymous broadcast Accounts for fluid network Bad link doesn’t hang whole system Isn’t this just fault-indifference?

Auctioneer monitors performance, renews contracts Prevents everyone from waiting on one broken

robot What if the auctioneer is faulty?

What could go wrong?

Rogue robot physically interferes with others Planning/execution problem, not allocation

problem Robot is dishonest about abilities

System assumes this never happens

Examples

Cost functions may be complex Based on distance traveled Based on time taken Some function of fuel expended, CPU cycles, etc.

Revenue based on completion of tasks Reaching a goal location Moving an object Etc.

Prices and Bidding

Robots can receive revenue from other robots in exchange for goods or services Example: haulage robot

If robots can produce more profit together than apart, they should deal with each other If one is good at finding objects and another is

good at transporting them, they can both gain

Simple Example 1: pickup task

5070

130

100

tA tB

Robot 1 50 100

Max Reward = 120

tA

Max Reward = 180

tB Bids Placed for Tasks

System cost: 50+70=120

tA tB

Robot 1 50 100

Robot 2 No bid 70

Profit: 70

Profit: 110

Robot 1

Robot 2

5070

tA tB tA+tB

Robot 1 70 80 110

Robot 2 No bid 110 170

Robot 2

Max Reward = 120

tA

Max Reward = 180



60

100


Robot 1

Robot 2

tA tB

Robot 1 50 100

Robot 2 No bid 70

Profit: 70

Profit: 110

Profit: 190

Profit: 0

Robot 1

Robot 2


100

130


5075

110

100

tA tB

Robot 1 50 100

Max Reward = 120

tA

Max Reward = 180



tA tB

Robot 1 50 100

Robot 2 110 75

Profit: 70

Profit: 105

Robot 1

Robot 2

5075

tA tB tA+tB

Robot 1 70 80 110


Robot 2

Max Reward = 120

tA

Max Reward = 180



60

60


Robot 1

Robot 2

tA tB

Robot 1 50 100

Robot 2 110 75

Profit: 70

Profit: 105

Profit: 190

Profit: 0

Robot 1

Robot 2

110

100



5075

110

100

tA tB

Robot 1 50 100

Max Reward = 120

tA

Max Reward = 180



tA tB

Robot 1 50 100

Robot 2 110 75

Profit: 70

Profit: 105

Robot 1

Robot 2

5075

tA tB tA+tB

Robot 1 70 80 No bid


Robot 2

Max Reward = 120

tA

Max Reward = 180



60

60


Robot 1

Robot 2

tA tB

Robot 1 50 100

Robot 2 110 75

Profit: 70

Profit: 105

Profit: 120+180-(50+60+110) : 80

Profit: 110 without even moving versusProfit: 165 at a system cost of 135

Robot 1

Robot 2

110

Simple Example 3: pickup task w/collaboration between robots

Suppose Robot 1 can not measure the path between tA and tBRobot 2 auctions tB to Robot 1 For 110

100

Simple Example 4: Pickup and bring home

5075

110

100

tA tB

Robot 1 50 100

Max Reward = 120

tA

Max Reward = 180



tA tB

Robot 1 100 No bid

Robot 2 No bid 150

Profit: 20

Profit: 30

Robot 1

Robot 2

5075

tA tB tA+tB

Robot 1 70 80 220


Robot 2

Max Reward = 120

tA

Max Reward = 180



7020


Robot 1

Robot 2

tA tB

Robot 1 100 No bid

Robot 2 No bid 150

Profit: 20

Profit: 30

Profit: 0

Profit: 110

Robot 1

Robot 2

110

100

Simple Example 4: Pickup and bring home

How Are Prices Determined?

Bidding Robots negotiate until price is mutually beneficial Note: this moves global solution towards optimum

Robots can negotiate several deals at once Deals can potentially be multi-party Prices determined by supply and demand

Example: If there are a lot of haulers, they won’t be able to command a high price

This helps distribute robots among “occupations”

Competition vs. Coordination

Complementary robots will cooperate A grasper and a transporter could offer a

combined “pick up and place” service Similar robots will compete

This drives prices down This isn’t always true:

Subgroups of robots could compete Similar robots could agree to segment the market Several grasping robots might coordinate to move

a heavy objects

Leaders

A robot can offer its services as a leader A leader investigates plans for other robots If it finds a way for other robots to coordinate

to maximize profit: Uses this profit to bid for the services of the robots Keeps some profit for itself

Note that this introduces a notion of centralization Difficult for more than a few robots

Why Is This Good?

Robust to changing conditions Not hierarchical If a robot breaks, tasks can be re-bid to others

Distributed nature allows for quick response Only local communication necessary Efficient resource utilization and role adoption Advantages of distributed system with

optimality approaching centralized system

Auction Based Multi-Robot Coordination

Example: Multi-Robot Exploration

Goal: explore and map unknown environment Environment may be hostile and uncertain Communication may be difficult Multiple robots:

Cover more territory more quickly Robust if some robots fail

Attempt to minimize repeated coverage Key: coordination

Maximize information gain, reduce total costs

Want robots to explore and map unknown area

Perception:

Unknown environment: How to estimate costs?

Do your best: assume something about the environment. (its clear)

LEARN!

Perception:

Unknown environment: Some sites may be inside obstacles!

Constantly update map information Constantly find new paths to site If no path, site is unreachable.

Perception

What is an obstacle and what is a teammate? Share your (x,y) location Set teammates’ positions as free space

Replanning: Reallocation of Sites

What happens when 1) robots miscompute costs 2) robots malfunction/die?

Subcontract expensive cities to other teammates

Completely offload sites to other teammates

zzzz

Communication

Original allocation of tasks Current position (x,y,t) to everybody New auctions for tasks (city location, bids,

winner, etc.) Completion of subcontracted tasks to

original owner

Architecture of the Market Approach

World is represented as a grid Squares are unknown (0), occupied (+), or empty (-)

Goals are squares in the grid for a robot to explore Goal points to visit are the main commodity exchanged in market

For any goal square in the grid: Cost based on distance traveled to reach goal Revenue based on information gained by reaching goal

R = (# of unknown cells near goal) x (weighting factor)

Team profit = sum of individual profits When individual robots maximize profit, the whole team gains

Example World

Exploration Algorithm

Algorithm for each robot:

1. Generate goals (based on goal selection strategy)

2. If leader is reachable, check with leader to make sure goals are new

3. Rank goals greedily based on expected profit

4. Try to auction off goals to each reachable robot If a bid is worth more than you would profit from

reaching the goal yourself (plus a markup), sell it

Exploration Algorithm

5. Once all auctions are closed, explore highest-profit goal

6. Upon reaching goal, generate new goal points

Maximum # of goal points is limited

7. Repeat this algorithm until map is complete

Bidding Example

R1 auctions goal to R2

Expected vs. Real

Robots make decisions based on expected profit Expected cost and revenue based on current map

Actual profit may be different Unforeseen obstacles may increase cost

Once real costs exceed expected costs by some margin, abandon goal Don’t get stuck trying for unreachable goals

Goal Selection Strategies

Possible strategies: Randomly select points, discard if already visited Greedy exploration:

Choose goal point in closest unexplored region Space division by quadtree

Benefit of Prices

Low-bandwidth mechanisms for communicating aggregate information

Map info doesn’t need to be communicated repeatedly for coordination

Information Sharing

If an auctioneer tries to auction a goal point already covered by a bidder: Bidder tells auctioneer to update map Removes goal point

Robots can sell map information to each other Price negotiated based on information gained Reduces overlapping exploration

When needed, Leader sends a map request to all reachable robots Robots respond by sending current maps Leader combines the maps by adding up cell values

An Experimental Setup

4 or 5 robots Equipped with fiber optic

gyroscopes 16 ultrasonic sensors

Three test environments Large room cluttered with obstacles Outdoor patio, with open areas as well as walls and tables Large conference room with tables and 100 people wandering

around Took between 5 and 10 minutes to map areas

Experimental Results

Experimental Results

Performance metric (exploration efficiency): Area covered / distance traveled [m2 / m] Market architecture improved efficiency over no

communication by a factor of 3.4

Market-based approach for multi-robot coordination is promising Robustness and quickness of distributed system Approaches optimality of centralized system Low communication requirements

Probably not perfect Cost heuristics can be inaccurate Much of this approach is still under development

Some pieces, such as leaders, may be too hard to do

multi-robot systems “the mob has many heads but no brains”. -- english proverb

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